Egg will cook with remaining heat in the last process. If you leave the heat on and wait for egg to be done, it will be too dry.

Mushrooms absorb lots of oil, but you don't need to use a lot of oil in this dish. When sauteed on slightly lower heat, mushrooms produce lots of liquid, which cooks the mushrooms.

Mixing a few kinds of mushrooms produces a complex taste. Eringi king oyster, shimeji, maitake and chanterelle are other good choices. To my taste, button mushrooms are too sour (OK if a small amount), while portabella mushrooms are too powerful for this dish.